Hitherto, there has been known an automatic transmission for a hybrid vehicle equipped with an international combustion engine and an electric motor (refer to, for example, Japanese Patent No. 3647399). According to the one disclosed in Japanese Patent No. 3647399, a dual clutch transmission (DCT) is used to employ any one gear train of an even ordinal gear shift stage in a transmission gear ratio rank order to run an electric motor at an appropriate rotational speed so as to carry out regeneration or assist when a vehicle is traveling at an odd ordinal gear shift stage in the transmission gear ratio rank order, or to employ any one gear train of an odd ordinal gear shift stage in a transmission gear ratio rank order to run the electric motor at an appropriate rotational speed so as to carry out regeneration or assist when the vehicle is traveling at an even ordinal gear shift stage in the transmission gear ratio rank order.